An atomic force microscope (hereinafter, referred to as AFM) is a device for obtaining a fine topographic image of the surface of a sample using, as a force detector, a cantilever having a sharp probe at its end (e.g., Patent Literature 1).
Specifically, when the probe is put close to the sample, a force of interaction works between the probe and the sample. When the force of interaction is detected, the vertical position of the probe for the sample is controlled to keep the force of interaction stable. When horizontally scanning the sample in this state, the probe goes up and down along the surface asperities of the sample with a certain distance between the probe and the sample. The AFM obtains a topographic image of the sample surface by recording the path of the probe with respect to a horizontal position.
Two operation modes: (A) static mode and (B) dynamic mode are known in the AFM. The two modes differ in how to detect the force of interaction between the probe and the sample using the cantilever.
The static mode AFM detects the force of interaction between the probe and the sample, based on the displacement of the cantilever caused by the force of interaction between the probe and the sample.
Meanwhile, the dynamic mode AFM detects the force of interaction between the probe and the sample when horizontally scanning the sample while mechanically oscillating the cantilever at a frequency close to the resonance frequency of the cantilever. This detection of the force of interaction is based on a change in oscillation amplitude, frequency, or phase caused by the force of interaction between the probe and the sample.
The method of concurrently measuring the potential distribution of the sample surface and the topographic image of the sample surface, using the AFMs is known (e.g., Non Patent Literature 1).
FIG. 8 is a schematic diagram showing the principle of a kelvin probe force microscopy (hereinafter, referred to as KPFM) generally known as a potential measurement device using the AFM.
As FIG. 8 shows, a KPFM800 includes a cantilever 804, an electrode in a probe shape (hereinafter, referred to as probe electrode) 823, a sample 805, an alternating-current power supply 801, and a direct-current power supply 852.
The cantilever 804 has the sharp probe electrode 823 at its end. One of the ends of the cantilever 804 which has the probe electrode is a free end. Moreover, the other end is a fixed end.
The sample 805 is an object to be measured and placed in the atmosphere or in the vacuum state.
The alternating-current power supply 801 is a power supply which applies an alternating-current bias voltage represented by Vac COS (ωmt) between the probe electrode 823 and the sample 805. Here, Vac is the amplitude of an alternating-current voltage, and ωm is the angular frequency of the alternating-current voltage.
The direct-current power supply 852 is a power supply which applies a direct-current bias voltage represented by Vdc between the probe electrode 823 and the sample 805.
The distribution of electric charges, polarizations, work functions, and others leads to potential distribution Vs in the surface of the sample 805. Therefore, Expression (1) below determines potential difference Vts between the probe electrode and the sample after the bias voltages are applied by the alternating-current power supply 801 and the direct-current power supply 852.[Math. 1]Vts=Vdc−Vs+Vac cos(ωn1t)  (Expression 1)
Here, one of the sides of the sample 805 is a front side facing the probe electrode 823. The other side is the back side of the sample 805. Furthermore, the coordinate axis which defines the direction from the back side to the front side as positive is hereinafter referred to as a z axis. Moreover, when Cts represents an electrostatic capacitance between the probe electrode and the sample, an electrostatic force Fes working between the probe electrode and the sample is determined by Expression (2) below.
      [          Math      .                          ⁢      2        ]                                                                                            F                  es                                =                                ⁢                                                      1                    2                                    ⁢                                                            ∂                                              C                        ts                                                                                    ∂                      z                                                        ⁢                                      V                    ts                    2                                                                                                                          =                                ⁢                                                      1                    2                                    ⁢                                                                                    ∂                                                  C                          ts                                                                                            ∂                        z                                                              [                                                                                            (                                                                                    V                              dc                                                        -                                                          V                              s                                                                                )                                                2                                            +                                                                        1                          2                                                ⁢                                                  V                          ac                          2                                                                    +                                              2                        ⁢                                                  (                                                                                    V                              dc                                                        -                                                          V                              s                                                                                )                                                                                                                                                                                                            ⁢                                                                            V                      ac                                        ⁢                                          cos                      ⁡                                              (                                                                              ω                            m                                                    ⁢                          t                                                )                                                                              +                                                            1                      2                                        ⁢                                          V                      ac                      2                                        ⁢                                                                  cos                        2                                            ⁡                                              (                                                  2                          ⁢                                                                                                          ⁢                                                      ω                            m                                                    ⁢                          t                                                )                                                                                            ]                                                                          (                      Expression            ⁢                                                  ⁢            2                    )                    
As Expression (2) shows, Fes contains: (i) direct-current components (the first and second terms of the right side of Expression (2)), (ii) ωm component of an alternating-current component (the third term of the right side of Expression (2)), and (iii) 2ωm component of the alternating-current component (the fourth term of the right side of Expression (2)).
Here, Fes can be measured as a displacement of the cantilever or a change in the oscillation amplitude, frequency, or phase of the cantilever. Moreover, the KPFM800 detects using a lock-in amplifier (not shown in FIG. 8), only the ωm component (i.e., the third term of the right side of Expression (2)) contained in the measured Fes.
As Expression (2) shows, the ωm component is proportional to (Vdc—Vs). Therefore, if feedback control is performed on Vdc so as to cancel the ωm component (reduce the ωm component to zero), the relationship Vdc=Vs always holds. A potential distribution image of the surface of the sample 805 can be obtained by causing the probe electrode 823 to horizontally scan the sample 805 in this state, and recording the value of Vdc with respect to the horizontal position of the electrode during the scanning.
As other potential measurement device using the AFM, a scanning Maxwell stress microscopy (hereinafter, referred to as SMM) is known.
The SMM measures a surface potential based on a principle similar to the principle used by the KPFM. Here, the only difference is in how to control the distance between the probe electrode and the sample. The KPFM controls, as with a typical dynamic AFM, the vertical position of the probe electrode 823 so that the change in the oscillation amplitude, frequency, or phase of the cantilever is kept constant. Meanwhile, the SMM controls the vertical position of the probe electrode so that the 2ωm component (the fourth term of the right side of Expression (2)) caused by the alternating-current bias voltage is kept constant.